The Improvement And Some Typical Application Of Smoothed Particle Hydrodynamics Method

Smoothed particle hydrodynamics (SPH) is a pure meshless method which has the Lagrange character. Comparing with traditional mesh-based methods, the SPH method can avoid the problems caused by mesh. For examples, the calculation would be interrupted because of mesh distortion during the process of numerical simulation of material large deformation by mesh-based methods; it's hard to simulate the strong discontinuity and shock wave problems by mesh-based methods; the mesh-based methods also have many difficulties in interface capture. The SPH method can treat these problems, mentioned above, naturally. The traditional mesh-based methods are hard to make further studies on the transient physical problems, such as explosion, penetration and high speed collision etc, which involve the processes of large deformation, strong discontinuity and interaction of material interface, because of the inherent deficiencies. Therefore, the studies on SPH method and its application to transient physical problems have important significance. However, it is still at its preliminary stage for the present SPH method, especially for its application to transient dynamics such as explosion. Some technical problems, such as numerical precision, stability and efficiency, still need to improve in the SPH method.This dissertation conducts a systematical research for the SPH method, and aims at doing some correction on the improvement of precision, stability and efficiency etc. The researches on improving the SPH method are the kernel and basis of the whole dissertation. Other parts of works in this dissertation are taking advantage of the SPH method to study the physical problems which involved the process of explosion. As a result, the following studies are carried out in this dissertation:(1) The based approximation and discretization processes of SPH method are formulated systematical. The efficiency of neighborhood particle searching process is compared between the direct searching algorithm and the tree searching algorithm. A correct material boundary searching algorithm is applied to SPH method. In the correct material boundary searching algorithm, the material boundary particle is determined by the detection of radian envelope. An extension virtual particle method is suggested to improve the numerical precision at free boundary. The extension virtual particles are generated by difference along the outside of free boundary. The mirror symmetry virtual particle method is employed to simulate rigid boundary. Some artificial correction terms of SPH method are also discussed. First, the ability of artificial viscosity in pressure oscillation handing and shock simulation is analyzed by the simulation of one dimension shock wave problem. Then, the artificial stress, which is used to remove the tensile instability, is tested through the two dimension rubber ring collision problem. After the discussion of artificial correction terms, a modified SPH method is constructed in the axisymmetric cylindrical coordinates. The feasibility and correctness of the cylindrical SPH method is verified by Taylor bar test.(2) The Riemann-solver based SPH method is extended to two-dimension coordinate. The purpose of adopting the Riemann-solver into SPH method is to manage the pressure oscillation at the discontinuous contact surface of shock problem. The function of Riemann-solver is used to correct the interaction between particles. Two numerical examples, shock tube and quasi-implosion problems, are simulated by traditional SPH and Riemann-solver based SPH method. The superior ability of Riemann-solver based SPH method in handing pressure oscillation is showed by the numerical results.(3) The SPH method is applied to investigate the process of explosion and explosively driven metal. The equations of state for charge and metal are employed in the SPH method to analyze the detonation process of charge and the large deformation process of metal. Two dimension linear shaped charge jet and explosively driven metallic tubes problems are used as numerical examples. The influences of different kinds of material yield models, which are employed in numerical examples, have been studied. The effects of different ignition mode for the performance of physical results have also been investigated in the examples. The detonation process is represented by SPH method, as well as the interaction process between explosive product and metal. From the numerical results, the advantages of SPH method in shock simulation, large deformation and fluid-solid coupling etc are demonstrated completely.(4) Multi-material hydrodynamic problem is simulated by SPH method. In order to trace the movement of the material interface, some corrections have been applied to SPH method. The corrections include state equation of idea gas, particle velocity and smoothed kernel etc. Two dimension gas (fluid) bubble problem and two-phase free surface flow problem are used to demonstrate the modified SPH method. Finally, an implementation of the SPH method is adopted to investigate underwater explosion problems. Numerical results represent the movement of free water surface, as well as interaction between shock wave and rigid wall in the problem of underwater explosion near air-water surface. The propagation of explosive wave under a given depth of water has also been captured. The simulations of under water explosion problems verify the feasibility of SPH method on the simulation of multi-material hydrodynamics under extreme condition.